We're having a party next week. This normally suggests that everything has already been arranged. We're going to have a party next week is also possible, with a similar meaning, but it might imply that there are still some minor arrangements to be made.
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ozzourtiWe have a party next week is not something I would use in this context. It doesn't sound natural to me.It's just about possible if, for example, a functions organiser is speaking of a scheduled event, but I agree that it doesn't sound natural in most contexts.